Concerto Simple Demonstration Test v4.b

# This is my first attempt to post a example of a test using Concerto 4 beta.

# This is an extremely simple test.  Too simple to be useful to most people yet I believe it is didactically helpful.

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The Following is the HTML code for Template 9. It is the form that the user first inputs answers to the three questions.

Template Description/Name: FixedSimpleQuestions

<p>Please Answer:</p>

<!--This displays each question.  The important thing to notice is the name of each text box, txt_1, txt_2, and txt_3-->
<p>1. 1+1=<input name="txt_1" type="text" /></p>

<p>2. 2+2=<input name="txt_2" type="text" /></p>

<p>3. 3+3=<input name="txt_3" type="text" /></p>

<p><input name="done" type="button" value="done" />​</p>

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The Following is the HTML code for Template 10. It is the form that the user receives feedback from.

Template Description/Name: FixedSimpleResults

<p>You got questions:</p>

<!-- Notice the values in {{}}.  These are the parameters passed to this template -->

<p>1. {{score1}}</p>

<p>2. {{score2}}</p>

<p>3. {{score3}}</p>

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# The Following is the R code that the test actually uses to run.

# We can see how R controls the flow of the user interface.

# Concerto Simple Test 1

# We call template 9, FixedSimpleQuestions, to be shown.  It can either be referenced by the template number of the name of the template.
items = concerto.template.show("FixedSimpleQuestions")

# Check if the items results are correct.  We can see that the responses to the items from the first template are saved within the list object item with the names txt_1, txt_2, and txt_3.
TF1 = items$txt_1==2
TF2 = items$txt_2==4
TF3 = items$txt_3==6

# Show the results to the user by feeding our item values as parameters back into the second template.
concerto.template.show("FixedSimpleResults", params=list(score1=TF1, score2=TF2, score3=TF3))

# I hope this gives you a feel for how easy it is to use Concerto to handle web based inputs.

# A powerful feature of Concerto is that it has functions that and query and modify tables using My SQL.

# More in future posts.

# I used an HTML encoder to translate my html code to post into blogger.

Generalized Graded Response Data Generating Command

# The following code will draw random test items from a graded response model.

# The command mat.binom will be useful in drawing a matrix of binomial results. I will use a command I programmed in a previous post. (http://www.econometricsbysimulation.com/2012/09/item-response-theory-estimation.html)
mat.binom <- function="function" n="n" p="p">  bin.mat <- p="p">  for (i in 1:nrow(p)) {
    for (ii in 1:ncol(p)) {
    # This will draw a random binomial for each of the probabilities.
    bin.mat[i,ii] <- i="i" ii="ii" n="n" p="p" rbinom="rbinom">  }
  }
 return(bin.mat)
}


rgrm <- d="1.7)" function="function" p="p" theta="0,a=cbind(rep(1,5),rep(1,5)),b=cbind(rep(0,5),rep(1,5)),">  # b is now an input matrix with each row representing a different item and each column representing a different grade for that item.  The number of columns should be equal to the maximum number of grades for all of the items.  Items may have less than the full number of grades indicated by NA values at upper levels.

  # We will use the grm Cululative Grade Function defined in a previous post as what we will use to generate our probabilities.
  # http://www.econometricsbysimulation.com/2012/09/generalize-graded-response-model.html
  grm <- a="1," b="c(0,1,2)," cplot="T," function="function" p="p" pplot="T," stackpoly="F" theta="1,">    ngrade = max(length(b),length(a))
    CGF = matrix(NA, ncol=ngrade  , nrow=length(theta))
    for (i in 1:length(theta)) CGF[i,] = exp(a*(theta[i]-b))/(1+exp(a*(theta[i]-b)))
    return(CGF)
  }

  # This will be the number of items to generate.
  if (sum(dim(a)!=dim(b))>0) warning()
  nitems = nrow(b)

  # This matrix will hold the results of the items.
  Y <- matrix="matrix" ncol="nitems)</p" nrow="length(theta),">
  rownames(Y) = paste("Stud", 1:length(theta))
  colnames(Y) = paste("Item", 1:nitems)

  for (i in 1:nitems) {
    # Draw the submatrix of a and b not equal to NA
    a.sub = !is.na(a[i,])
    b.sub = !is.na(b[i,])
    # Draw a uniform draw for every individual
    unif.draw = runif(length(theta))
    # Spread those draws out into a matrix for each grade of each item for each individual
    unif.draws = matrix(unif.draw, ncol=length(a.sub), nrow=length(theta))
    # Draw the probability of getting each grade for each item
    itemi = grm(theta=theta, a=a[i,a.sub], b=b[i,b.sub])
    # Calculate the grade for each item.
    Y[,i]<-apply itemi="itemi">unif.draw,1,sum)
    # Since the grm function creates a matrix with the probability of getting that value or more for each grade we can simply count the number of times that the random uniform draw got below that value.  If the draw is low enough then the student gets full credit.  If it is high enough then the student gets no credit.
  }
  # Specify the command's return value
  return(Y)
}

# Notice, theta can be any length but a and b must have the same dimensions
a=cbind(rep(1,6),rep(1,6),rep(c(NA,1),3))
b=cbind(rep(1,6),rep(2,6),rep(c(NA,3),3))
# This will create six items with grades from 1 to 2 and 1 to 2 to 3.  The NA's mean that grade is missing (undefined).

# The length of theta is equal to the number of students
theta=seq(0,7,.5)

rgrm(theta=theta,a=a , b=b)
-apply>->->->->->->